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Numerade Educator



Problem 22 Hard Difficulty

Perform the indicated operations.


$\therefore(x-1)(x+2)(x-3)=x^{3}-2 x^{2}-5 x+6$


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Video Transcript

So we're gonna be doing the days we're actually gonna be doing a product of three. Binomial sze looks kinda hard at first, but it's a process of simple steps said you just gotta do once and then keep on beating. So we're fresh gonna do is we're gonna separate the three by no meals into to it doesn't matter which too. I'm gonna go ahead and do the 1st 2 because they're already here. Someone drawing a line here to go ahead and separate them. Now I'm gonna do is distribute. So with distribution, you're gonna multiply all the terms in your first binomial into your second someone take my ex terms and multiply them together and it's gonna go ahead and give me X squared and then go ahead and do the 1st 1 with the last one. Just give me a positive. I'm moving forward to do the same thing just with the other two terms. So negative one and excuse me a negative one and negative one and deposited to gives you native to. So now we're left with this polynomial of four terms. Don't have that by no means I'll be here to turn so what we gonna do before we go on? We want to go ahead and combine some of these, like terms to make this pond on you a little bit easier. You can see that you have these two with the same degree of their variable, so you can go out and combine those off plus to minus one. So it reduces down to two a x word. I'm sorry. Plus X minus two and then, you know, go ahead and leave that paired up with the binomial of ex ministry. Now we're gonna go ahead and do the same thing. But just to make my life a little bit easier, I'm gonna go in and use this first because a lot easier to most by two things three times than three things two times. So just like we did up here, we're gonna go ahead and multiply out using the distribution property, which means everything in this fallen up in this final Milne symbols. Clever everything in this trying time. So first we'll start with the X and multiply it times X squared. That's gonna give me an excuse and X where the next give me a plus X squared and then the necks with the negative to me in negative two X. So now we went ahead and did the first term. Now we can go ahead and do the second term, which is a negative three. So negative three times x squared. So now here's where you can actually do two different names. Traditionally, people continue to write it down and give you one long sentence. One thing that I like doing make myself easier. Since I can see that I'm gonna go ahead and get a term here with the square has the exponents. I can see the square as the ones that have already written. And I'm gonna go ahead and write my answer down here and you'll see what I'm doing. That it just a bit Once we finish this fool multiplication here. So I get the negatives three times the X, Give me a negative three X and native three times six gives me a negative positive six. I'm sorry. Now we notice after we did the 2nd 1 my degree terms light up in there all the same. So we noticed there's no other term here with X Cube, so it's gonna be the only excuse that I have. Similarly, the only constant that we have is gonna be the plus six. No, it makes it easier. Could I just have a plus X squared minus three. X square just gives me a minus two x squared in the minus two x plus the negative three. Excuse me. And minus just this one little step makes it a little bit easier than rather than having to get everything over here. And I'm just gonna write it out real quick so you can see what that would look like since that I haven't go through here and making match. It's a little bit easier to read going vertically. So in the end, you know, calling the all male sport terms with the degree of three. After we multiply the three quantities out here, um, any other questions feel free And then, you know, thank you